In a time-dispersive communication channel, such as a magnetic storage channel, it is advantageous to filter the channel to provide an equalized channel response which, when synchronously sampled in the absence of noise, provides nonzero integer-valued samples over a limited span. When the span of the equalized response is more than one symbol period in response to a single input, the responses of sequential inputs interfere with one another, and the equalized channel is referred to in the literature as a partial response channel. Partial response channel models, such as a dicode partial response channel, a class-IV partial response (PR4) channel, or an extended class-IV partial response (EPR4) channel, are of particular interest in magnetic recording.
When the output of a partial response channel is synchronously sampled, the response to a given channel input is dependent on the current input and previous channel inputs whose nonzero response is within the interference span of the equalized channel. Each output sample is corrupted by additive noise, which is often assumed to be Gaussian.
For purposes of the following discussion, it is convenient to associate a sequence of symbols, such as {u0, u1, u2, . . . } with the corresponding D-transform of the sequence,
            U      ⁡              (        D        )              =                  ∑                  i          =          0                ∞            ⁢                        u          i                ⁢                  D          i                      ,where ui is the ith symbol in the sequence and D is the unit delay operator.
FIG. 1 is a simplified diagram of a typical partial response receiver for magnetic recording channels. The sequence of binary user inputs U(D) is the input to a magnetic channel 100 with time domain dibit response h(t). The output of the channel is corrupted by wideband, additive noise. Analog lowpass filter 101 band-limits the received signal to prevent aliasing in sampler 102. The sampler may be either an analog-to-digital converter, or may alternatively be an analog sample-and-hold circuit. The stream of samples enters equalizer 103, which is typically a finite-impulse-response (FIR) filter. Optionally, equalizer 103 may be adaptive to refine the channel response.
In an ideal system with perfect gain, equalization, timing, and without noise, the combined response of 104 is the desired system partial response polynomial, P(D). The output of the ideal noiseless partial response channel is given by X(D)=U(D)P(D). A partial response polynomial of the form P(D)=(1−D) (1+D)R is commonly utilized in a magnetic recording system, where R is a non-negative integer. When R=0, P(D)=1−D, and the system is known as a dicode partial response channel. For a PR4 system, R=1 and the partial response polynomial is P(D)=1−D2; for EPR4, R=2 and P(D)=1+D−D2−D3.
In a real system, the output of the partial response channel is Y(D)=X(D)+E(D), where the various channel imperfections observed at the ith output of the system are lumped into an error term, ei. Under the assumption that channel imperfections are due to conditions which vary slowly as compared to the bit rate of the system, the average channel quality over the most recent observed span of K samples may be monitored. One such method of monitoring channel quality obtains an estimate of the average error variance over a span of K samples in a moving average estimator as shown in FIG. 2.
In the typical receiver of FIG. 1, sampling errors are minimized with decision-directed control loops, which adjust for variations in channel amplitude, timing phase error in sampling, and a misadjusted equalizer. In particular, the performance of the timing recovery loop is critical. The achievable adaptation rate of these control loops is highly dependent on loop delay, and adaptation rates must be reduced for long delays to maintain control loop stability.
The present disclosure relates to methods of estimating the noiseless response of the partial response channel in a detector. Various prior art detection methods for partial response channels are known in the literature. A typical prior art detector of the noiseless channel output sequence for control loop purposes is a slicer, which relies on the expected integer-valued output of the channel. For example, a dicode channel produces noiseless channel outputs of −1, 0, and +1 in the absence of noise. By comparing the sampled channel output to set thresholds of −0.5 and 0.5, for example, a slicer is able to make sample-by-sample estimates of the nearest channel output in the set of all possible noiseless channel outputs. The slicer simply regards the partial response channel as a multi-level communication system, and the ith detector decision is based solely on the observation of the ith noisy channel output.
Another prior art detector is known as a Viterbi detector, which performs maximum likelihood sequence estimation using a multi-state detector, where each state represents a possible combination of interfering channel inputs, in order to fully realize the Viterbi detector's gain, the final decisions of the Viterbi detector typically incur a delay several times the interference span of the channel. A slicer-based detector ignores constraints on the sequence of noiseless outputs of the system imposed by properties of the partial response channel, and tends to have a higher estimation error rate than detectors utilizing this sequence information, such as the Viterbi detector.
Decision-directed control loops typically utilize the estimate of the noiseless response of the channel to estimate gain error, timing error, and equalization error. When the slicer-based detector makes erroneous estimates too often, it further corrupts the estimates used to adjust the channel in the decision-directed control loop. In a noisy environment with a high slicer-based detection error rate, timing recovery may be lost, leading to catastrophic error.
Although the Viterbi detector has improved immunity against noise, two salient features of the Viterbi detector make it less typical as a detector in a decision-directed control loop. First, the Viterbi detector typically has long decision delay. The long inherent delay of the Viterbi detector reduces the adaptive performance of a decision-directed control loop. Second, when erroneous tentative decisions are made in the Viterbi detector, internal feedback of state metrics results in final decisions that contain bursts of multiple estimation errors. When decisions of the Viterbi detector are burstily erroneous, these bursts threaten to further corrupt control of the receiver.
In view of the foregoing, a need exists in the art for a general estimation method for the noiseless output of a partial response channel in decision-directed control loops with reasonable delay, with improved immunity against noise, and with limited error propagation.